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Numerical Simulation of Javelin Best Throwing Angle Based on Biomechanical Model

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Numerical Simulation of Javelin Best Throwing Angle Based on Biomechanical Model id245857953 pdfMachine by Broadgun Software - a great PDF writer! - a great PDF creator! - http://www.pdfmachine.com http://www.broadgun.com BBiiooTTISSNe e: 097cc4 - h7h435 nnoolVlolouome g8g Issuyye 8 An Indian Journal FULL PAPER BTAIJ, 8(8), 2013 [1042-1047] Numerical simulation of javelin best throwing angle based on biomechanical model Xia Zeng*, Xiongwei Zuo Department of Physical Education, Changsha Medical University, Changsha 410219, (CHINA) E-mail: [email protected] ABSTRACT KEYWORDS This paper uses the motion aerodynamics principle to analyze the javelin Biomechanics; flight process, integrates related factors with athletic performance in the Aerodynamics; study of the force condition and movement condition of the human body Throw angle; and the javelin, numerically simulates the different angles of fixed param- Mathematic numerical eters by Mathematic software, obtains the theoretical optimum throwing simulation. °, that is when the shot angle is 40° and the angle of the javelin’s angle 40 ° the throwing distance reaches long axis with the horizontal surface is 31 the greatest. The results are very consistent with the actual situation; this ’s article can make reasonable suggestions for the promotion of this project athletic performance, provides a theoretical basis for the javelin sports technique, and confirms the reasonableness of existing theory and tech- nique. 2013 Trade Science Inc. - INDIA INTRODUCTION ing sport biomechanics and aerodynamics principle to conduct objective analysis of the javelin throwing move- In the javelin movement, moving trajectory and ment has an actively promoting effect on the develop- moving results of javelin are primarily reflections of a ment of sports technology. set of human movement. Using the biomechanical prin- Javelin throwing process includes: run-up, final force ciples can reasonably prove the maturity of the tech- and javelin releasing flight three phases, where the run- nique and correct errors of technique. When the javelin up phase takes the longest time, and this stage provides releases from the hand it suffers the gravity and air re- the best posture for throwing and at this foundation stage sistance. Due to its shape and mass, it determines that the role of initial kinetic energy is related to achieve- the air resistance of the javelin during movement in the ments; final stage is also used to provide the initial ki- air cannot be ignored, so when we study the moving netic energy for the javelin flight, but its effect is far bet- trajectory of javelin after disposing the aerodynamics ter than the run-up phase, this stage also provides the principle is a good theoretical tool. Only by combining throwing angle of javelin flying, which is critical stage the kinetic characteristics and moving trajectory of the related to athletic performance; During flight javelin re- javelin after disposing can we determine the best shot ceives air resistance and gravity, although the results do angle and speed combination of javelin. Therefore, us- not have a subjective relation, but it provides result refer- BTAIJ, 8(8) 2013 Xia Zeng and Xiongwei Zuo 1043 FULL PAPER ence for the research of validity and rationality of first equivalent to the braking point, as shown in Figure 2. two phases. In this paper, through biomechanics theory and the aerodynamics theory, it conducts a detailed analysis for the three stages of javelin throwing movement, con- firms the reasonableness of the existing technique of this movement combing with the analysis results, and Figure 2 : Schematic of the forearm rotates relatively around provides rationalization proposals for the scientific the elbow joint training. The rotation moment of momentum of the forearm relatively around Point B is as formula (1): SPORTS MECHANICAL ANALYSIS OF LAST â M = I (1) FORCE TECHNIQUE (TAKE THE RIGHT 2 In Formula (1) M represents the torque generated HAND THROWING FOR EXAMPLE) â in the forearm muscle contraction, represents the an- The final stage of javelin throwing technology starts gular acceleration of the forearm around point B. from the right foot, through series of actions delivering According to the definition of angular acceleration by the legs, hips, torso, shoulder, elbow, and hand, and the angular momentum theorem can be obtained as for- finally throw out the javelin. The duration time of the mula (2) below: final stage is about 0.12s-0.15s, which is very short 2 1 M t I 2 ( 2 1 ) (2) from the time interval. But force sequence and speed t Ä change of all aspects of the body are consistent with In Formula (2) t shows the action time of forearm the biomechanics whipping principles. In the braking muscles torque M; by the formula (2) the expression of ù process it has shown a very large instantaneous im- angular velocity 2 can be obtained as formula (3): pulse, makes the javelin have greater instantaneous M t momentum, thus it can have a high initial kinetic energy. 2 1 (3) I 2 In the throwing arm whipping process, when the The formula (3) shows that the angular velocity of hand, forearm and upper arm are in the same line, the ù the forearm is increasing on the basis of in the pro- three links do not exist the relative rotation, but have 1 cess whipping of throwing arm, and the increased value the same angular velocity relative to the shoulder axis, M t as shown in Figure 1. is . I 2 When the rotation angle of forearm around point B is very small, according to the relationship of angular and linear velocity, we have the expressions in formula (4): Figure 1 : The simple schematic when the arm is in straight v r 1 1 1 line v r v r r 2 2 2 1 2 2 (4) In Figure 1 Point A represents the shoulder joint, v v1 v 2 í point B represents the elbow joint, point C represents In Formula (4) represents the linear velocity of í the wrist joint, I1, I2 respectively mean the moment of the point C in wrist relatively to the shoulder joint, ù 1 inertia of upper arm and forearm, 1 means the angular represents the linear velocity of the point B in elbow velocity of the arm rotates straightly around the shoul- í joint relatively to the shoulder joint, 2 represents the der joint. But in the throwing process, forearm and up- linear velocity of the point C in wrist relatively to the per arm has the relative rotation. We suppose the fore- elbow joint, and r , r respectively represents the length arm rotates around the elbow point B, where point B is 1 2 of the upper arm and forearm. BiioTechnollogy An Indian Journal 1044 Numerical simulation of javelin best throwing angle based BTAIJ, 8(8) 2013 FULL PAPER Substitute the formula (2) and (3) into the formula AERODYNAMIC ANALYSIS (4) formula (5) can be obtained: r M t After disposing in addition to its own gravitational v (r r ) 2 1 1 2 (5) force Javelin also suffers air resistance. Studying the I 2 movement condition of javelin releasing can reflect the According to formula (5), when forearm whips, the relationship between movement characteristics and ath- r M t 2 letic performance when releasing the Javelin, and it is line speed of the wrist increases by I comparing ’s throwing tech- 2 the entry point to study the movement with no whipping. nique problem of non-forces influencing factors, so it is ’s center of gravity In the final force stage, the body necessary to study the movement of the javelin after speed is constantly declining; human kinetic energy is disposing. also reducing. The direction of the braking by the left For any one kind of javelin it has its fixed shape leg landing and the inertia by the throwing arm on the and quality. We can use the polynomial fitting way to javelin in the acceleration process is opposite to the dispose each measurement point, and get the physical ’s speed acceleration direction of the javelin. So the body characteristics parameters of the javelin. This paper is declining, if in the last throwing process of throwing takes the javelin for adult males as the research object, arm, throwing objects, the stronger the force of inertia uses the previous 4 order polynomial function as a model of the throwing matter is, the much thorough that mo- base below. The javelin physics parameters in TABLE mentum transfer of the body on the javelin is. 1 can be obtained. TABLE 1 : Javelin physics parameter table for adult male Parameter name Physical magnitude Total mass of Javelin 811.5g Distance from the gun breech to the centroid 1585mm Distance from centroid to gun head 1055mm × Surface area of Javelin 2.098 105mm2 × The maximum projected area of javelin 6.352 104mm2 × The rotational moment of inertia around its own shaft (the axis perpendicular to the javelin direction) 0.4563 109g*mm2 × The rotational moment of inertia around its own shaft (the axis along the javelin direction) 0.1379 106g*mm2 × The rotational moment of inertia around its own shaft (another axis perpendicular to the javelin direction) 0.4563 109g*mm2 The initial kinetic parameters when releasing javelin include: the shot height of javelin centroid is h , the shot í 0 velocity of centroid is , the angle of javelin centroid 0 è shot velocity with the horizontal surface is , the angle á 0 of javelin with the horizontal plane is , the pitch angu- 0 ù lar velocity when releasing the javelin is 0, the angle of the projection of the javelin long axis in the xoy surface and the projection of the javelin centroid velocity in the ã xoy surface is generally known as the yaw angle, the 0 Figure 3 : The initial state of javelin releasing instant in the releasing moment of the javelin is in the spatial coordi- coordinate system nate system as shown in Figure 3: Javelin suffers gravity vertically downward and re- expression of the friction resistance is in formula (6): sistance generated by air during movement in the air.
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